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Hello,
I've played with some data in a speadsheet but have no idea if I've even come close to to calculating Cs properly.
I also don't know what a good number looks like - woul it be similar to Cp, meaning am I looking for a 1.33 or better? How would we calculate control limits?
Does anyone have a spreadsheet that does the calculation? I'm very interested in any known test data and results someone might have so I can prove out my sheet/calculations.
I'm using the calculation: Cs = min{USL - Mean, Mean-LSL}/{3*[sigma^2+(Mean-Target)^2+abs(3rd_Moment/sigma)]} (thanks Darius!)
Attached is my worksheet. Am I even close??
I kind of put it together leveraging information from a you tube video as this formula is my first introduction to moments/skew/kurtosis:
SIDE NOTE: I've searched for an article I had been pointed to before (EVALUATION OF PROCESS CAPABILITY INDEX FOR NON-NORMAL DISTRIBUTIONS) but have not turned it up.
I've played with some data in a speadsheet but have no idea if I've even come close to to calculating Cs properly.
I also don't know what a good number looks like - woul it be similar to Cp, meaning am I looking for a 1.33 or better? How would we calculate control limits?
Does anyone have a spreadsheet that does the calculation? I'm very interested in any known test data and results someone might have so I can prove out my sheet/calculations.
I'm using the calculation: Cs = min{USL - Mean, Mean-LSL}/{3*[sigma^2+(Mean-Target)^2+abs(3rd_Moment/sigma)]} (thanks Darius!)
Attached is my worksheet. Am I even close??
I kind of put it together leveraging information from a you tube video as this formula is my first introduction to moments/skew/kurtosis:
SIDE NOTE: I've searched for an article I had been pointed to before (EVALUATION OF PROCESS CAPABILITY INDEX FOR NON-NORMAL DISTRIBUTIONS) but have not turned it up.
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, but I think is a handy way to do it.

Well maybe, just because, the minimum value is domed is this case to be depending from the LSL, maybe, if is no possible the 0, it should not be considered. I will do some tests and tell you my conclusions.
0.68 and 0.95 are the values for “bell shaped” distribution, 68% of the data are between +/- 1 sigma, the 95% of the data are between +/-2 sigma. I know is used in this case for non parametrics (it can be called half-parametrical method).
The method I outlined take the distribution in two halves (using the median), and the ds_up is calculated as it was a normal distribution but taking just one side in account at the time (for ds_up the upper side, for ds_dwn the lower ones). It may sound weir but I worked with it and found it to work fine for me, I saw sometime ago a method that used the percentile for the percentage at +/- 3 sigma to determine the control limits (ones again …, a half-parametrical method), and it can be done that way, but for data with many “outliers”, found this method more robust (the outliers doesn't have any effect). As I told you is a method I tested (and created), you can simulate data that behave as gamma and work fine. I even use it for outlier detection on a "modificated chauvenet" (by me),method.
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Works great! Thank you very much!!